Question

Найдите cos^2a,если sin3a/sina + cos3a/cosa =1​

Answer 1

$\dfrac{sin3a}{sina}+\dfrac{cos3a}{cosa}=1\\\\\\\dfrac{sin3a}{sina}+\dfrac{cos3a}{cosa}=\dfrac{sin3a\cdot cosa+cos3a\cdot sina}{sina\cdot cosa}=\dfrac{sin(3a+a)}{\frac{1}{2}\cdot sin2a}=\dfrac{2\cdot sin4a}{sin2a}=\\\\\\=\dfrac{2\cdot 2sin2a\cdot cos2a}{sin2a}=4\cdot cos2a=4\cdot (cos^2a-sin^2a)=\\\\\\=4\cdot (cos^2a-(1-cos^2a))=4\cdot (2cos^2a-1)=1\\\\\\2cos^2a-1=\dfrac{1}{4}\\\\\\2cos^2a=\dfrac{5}{4}\\\\\\cos^2a=\dfrac{5}{8}\\\\\\Otvet:\ \ C)\ .$